Question

Two boats on opposite banks of a river start moving towards each other. They first pass each other 1400 meters from one bank. They each continue to the opposite bank, immediately turn around and start back to the other bank. When they pass each other a second time, they are 600 meters from the other bank. We assume that each boat travels at a constant speed all along the journey. Find the width of the river?

Answer 1

Let xx be the width of the river. It is given that, when they have met the first time, boat11 has travelled 14001400 m and boat22, (1400−x)(1400−x) metres.

When they meet for the second time, boat11 has travelled 600+(x−1400)=(x−800)600+(x−1400)=(x−800) m, and boat22, 1400+(x−600)=(x+800)1400+(x−600)=(x+800) m.

Note that, the relationship of the distances each traveled, is the same to both meetings. Thus,

14001400−x=x−800x+80014001400−x=x−800x+800⇒x=?⇒x=?Hope you can take it from here.

Answer 2

S1*t1 = 1400 : S1 speed of boat 1, t1 : time to do 1400 meters(boat 1)1400 + S2*t1 = X : S2 speed of boat 2S1*t2 = X + 600 : t2 time to do X + 600 (boat 2)S2*t2 = 2X - 600S1 = 1400/t1S2 = (X-1400)/t1T = t2/t1 : definitionsubstitute S1, S2 and t2/t1 using the above expressions in equations 3 and 4 to obtain1400*T = X + 600X*T - 1400*T = 2X - 600 : 2 equations 2 unknownsEliminate T and solve for X to obtain X = 3600 meters.